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There is a moment in a long relationship that nobody warns you about. Nothing has gone wrong. Nobody cheated, nobody shouted, nobody left. You just notice one ordinary Tuesday that the feeling is quieter than it used to be, and you start quietly wondering whether that means something is broken.
It turns out mathematicians have been studying that exact moment for about thirty years. And the first thing you learn from the mathematics of love is oddly comforting: in almost every model ever built, the fading is not the problem. It is the starting assumption.
What the mathematics of love actually measures
Laurent Pujo-Menjouet, a professor at the University of Lyon I, has spent years working with mathematicians around the world on models that treat a couple the way physics treats a swinging pendulum or a cooling cup of tea — as a system that changes over time according to rules. His book on the subject, Love! Valour! Equations!, was published this year by Routledge.
The models are simpler than you would expect. According to the publisher’s summary of the work, three ingredients do most of the heavy lifting: the partners’ mutual attraction, the natural erosion of feelings over time, and the way each person reacts to the other’s emotions. Outside pressure gets added on top — work, illness, money trouble, raising children.
Run those together and you get something the researchers describe as a threshold. If feeling drops below a certain line and stays there, the mathematics points toward separation. Above it, the system can absorb a surprising amount of damage and recover.
The equations were never built for love
Here is the part that made me sit up. These are not new equations written for romance. They are borrowed.
The family tree runs back through Malthus, who was modelling how populations grow and run out of food, and through the Lotka-Volterra equations, which were built to describe predators and prey — how a population of lynx rises and falls against a population of hares. In the 1990s the psychologist John Gottman took that machinery, applied it to couples by coding their actual interactions, and showed it could predict outcomes.
So the mathematics currently being used to describe your marriage was originally designed to describe how many rabbits get eaten. Nobody set out to insult anyone. It is just that the maths of two things affecting each other over time turns out to be the same maths, whether the two things are animals in a valley or two people in a kitchen.
That matters more than it sounds. Because equations built for predators and prey have no concept of feeling at all. They only track behaviour — what one side does, what the other side does back, and how fast.
The fading is an assumption, not a discovery
Read the three ingredients again and look at the middle one: the natural erosion of feelings over time.
That is not something the models found. It is something the models were told. It is written in as a constant before a single real couple is measured, the same way you would write in gravity before modelling a falling stone. Every version of these equations, from every research group, starts from the assumption that intensity decays on its own unless something acts against it.
Which means the question the mathematics is actually asking is not "why did the feeling fade?" The fading is the background condition, as unremarkable as a cup of tea going cold. The question is: what, if anything, is putting heat back in?
That reframes an enormous amount of private misery. A lot of people quietly conclude that a cooling feeling is a verdict on whether they chose the right person. In the models it is not a verdict at all. It is Tuesday.
It also explains why a relationship can be lonely without being bad, and why that particular loneliness is so hard to name out loud. Being lonely inside a marriage is a specific kind of alone, and it is not evidence that the marriage was a mistake.
The one variable you actually control
If attraction is largely given and erosion is assumed, that leaves the third ingredient: how each person reacts to the other’s emotions. And this is where the models get genuinely practical.
A group of researchers in Poland added a term for something the earlier equations ignored — delayed reactions. Not whether you react, but how long you take before you do. In their work, the time a person spends thinking about a conflict before responding can either intensify the tension or defuse it.
Sit with that. In a system where two of the three main levers are more or less out of your hands, the one that is fully yours is the gap between being hurt and answering.
Not what you feel. Not even what you eventually say. The pause.
Anyone who has ever sent the message at 11pm and reread it at 7am already knows this in their body. The delay is not avoidance. It is the only lever in the machine with your hand on it.
The same principle explains why some arguments burn out in ten minutes and others smoulder for a decade. It is rarely the subject. It is the speed of the return volley — and, sometimes, a mind that will not stop replaying something long after the conversation ended, which is its own well-documented trap and the reason looping on a partner’s past is so hard to switch off.
What the researchers say the models cannot do
This is the part most write-ups skip, and it is the part that makes the rest trustworthy.
The researchers state plainly that these models are built mainly on Western relationship patterns, so they do not necessarily describe how love works everywhere. They also say that human behaviour is unpredictable and often irrational, and that the models predict tendencies, not certainties.
No equation is going to tell you whether to stay. It was never designed to. What it can do is describe the shape of a slope — and tell you which direction is uphill.
An older description of love does exactly the same thing
Here is the odd part.
The most-read description of love in the world is an ancient letter, recited at more weddings than any other passage on earth, including by people who are not religious in the slightest. And it never once tells you what love feels like.
It is a list of behaviours. Patient. Kind. Not envious. Not boastful. Not easily angered. Keeping no record of wrongs. Every item is something a person does, and a striking number of them are things a person deliberately does not do.
And the very first word on that list is patience — which in the older languages carried the sense of being slow to anger. Long-tempered. A long fuse.
Which is to say: thousands of years before anyone wrote a differential equation for a marriage, someone had already identified the same variable the researchers in Poland added. Not the feeling. The gap before the answer. Whether you believe that instruction came from centuries of accumulated human experience or from God, it is the oldest piece of relationship advice we have, and it has outlasted every theory that replaced it.
The mathematics arrived at it in the 1990s. The letter got there first.
What to do with this
None of this requires money, an app, or an appointment. It costs nothing but timing.
- Put a gap in. When something stings, decide in advance how long you will wait before responding — ten minutes, or until after a meal. Say out loud that you want to think first, so the pause reads as care rather than as the silent treatment.
- Stop treating the cooling as evidence. A quieter feeling is the baseline the models assume. Ask what is adding warmth back, not what went wrong.
- Add heat deliberately. In the equations, the only thing that counters erosion is input. Small, repeated, unremarkable input beats one grand gesture a year.
- Learn your own default speed. Some people fire back instantly, some withdraw for days, and both are reaction times. Our free What Is My Conflict Style? quiz is a fast, honest way to see which one you are.
A question worth arguing about
If a mathematical model could genuinely tell you, with reasonable accuracy, which way your relationship was heading — would you want to be told? Or is not knowing part of what makes people keep trying? Tell me what you would choose in the comments. I suspect people split almost evenly on this one.
If this said something you have been trying to say
- Mathematicians who model long-term love build the fading of feeling into the equation as a given. It is the starting assumption, not the finding. The variable they say actually decides things is how long you wait before you answer. https://bgodinspired.com/index.php/relationships-and-family/mathematics-of-love-why-feelings-fade/
- The equations now used to model marriages were originally built to describe predators and prey. They have no concept of feeling at all — only what one side does, what the other does back, and how fast. https://bgodinspired.com/index.php/relationships-and-family/mathematics-of-love-why-feelings-fade/
- Two of the three main levers in the mathematics of love are largely out of your hands. The one that is fully yours is the gap between being hurt and answering. https://bgodinspired.com/index.php/relationships-and-family/mathematics-of-love-why-feelings-fade/
Questions people ask about the mathematics of love
What is the mathematics of love?
The mathematics of love is the use of dynamical-systems equations to describe how romantic relationships change over time. Models developed by Laurent Pujo-Menjouet at the University of Lyon I and by researchers elsewhere treat a couple as a system governed by three main factors: mutual attraction, the natural erosion of feelings over time, and how each partner reacts to the other’s emotions. External pressures such as work, illness, money problems and children are added on top. The researchers stress that these models predict tendencies, not certainties.
Do mathematical models say feelings always fade in a relationship?
The models assume it rather than prove it. The gradual erosion of feeling is written into the equations as a starting condition before any couple is measured, in the same way gravity is written into a model of a falling object. So a cooling feeling is treated as the normal background state, not as a sign that something has gone wrong. What the models then examine is what, if anything, counteracts that erosion.
Where did the equations used to model relationships come from?
They were borrowed from population biology. The lineage runs through Malthus’s work on population growth and the Lotka-Volterra predator-prey equations, which describe how two populations rise and fall in response to each other. In the 1990s the psychologist John Gottman applied that mathematical approach to couples by coding their real interactions and showed it could predict relationship outcomes.
What single factor do the models say matters most?
How each partner responds to the other, including how quickly. Researchers in Poland added a delayed-reaction term to the equations, recognising that the time a person takes to reflect on a conflict before responding can either intensify or defuse the tension. Since attraction and natural erosion are largely fixed inputs, the response — and specifically the pause before it — is the variable most under an individual’s control.
Can maths predict whether a relationship will last?
No. The researchers behind these models state that they are based primarily on Western relationship patterns and that human behaviour is inherently unpredictable and irrational. The models describe tendencies across many relationships rather than outcomes for any specific couple, and they are a tool for understanding the shape of a relationship’s dynamics, not a forecast for an individual.
